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The outliers would greatly change the estimate of location if the arithmetic average were to be used as a summary statistic of location. The problem is that the arithmetic mean is very sensitive to the inclusion of any outliers; in statistical terminology, the arithmetic mean is not robust.
Also referred to as frequency-based or counting-based, the simplest non-parametric anomaly detection method is to build a histogram with the training data or a set of known normal instances, and if a test point does not fall in any of the histogram bins mark it as anomalous, or assign an anomaly score to test data based on the height of the bin ...
CONN preprocessing pipeline includes steps designed to estimate and correct effects derived from subject motion within the scanner (realignment), correct spatial distortions due to inhomogeneities in the magnetic field (susceptibility distortion correction), correct for temporal misalignment across slices (slice timing correction), identify potential outlier images within each scanning session ...
The idea behind Chauvenet's criterion finds a probability band that reasonably contains all n samples of a data set, centred on the mean of a normal distribution.By doing this, any data point from the n samples that lies outside this probability band can be considered an outlier, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size ...
Grubbs's test is based on the assumption of normality. That is, one should first verify that the data can be reasonably approximated by a normal distribution before applying the Grubbs test. [2] Grubbs's test detects one outlier at a time. This outlier is expunged from the dataset and the test is iterated until no outliers are detected.
Others are model-based. Box plots are a hybrid. Model-based methods which are commonly used for identification assume that the data are from a normal distribution, and identify observations which are deemed "unlikely" based on mean and standard deviation: Chauvenet's criterion; Grubbs's test for outliers; Dixon's Q test
Previously when assessing a dataset before running a linear regression, the possibility of outliers would be assessed using histograms and scatterplots. Both methods of assessing data points were subjective and there was little way of knowing how much leverage each potential outlier had on the results data.
OPTICS-OF [5] is an outlier detection algorithm based on OPTICS. The main use is the extraction of outliers from an existing run of OPTICS at low cost compared to using a different outlier detection method. The better known version LOF is based on the same concepts.